The volume of a container measures 4,000 mm3 and contains 50 marbles. Each marble has a radius of 2 mm. Use 3.14 as an approximation for pi. How much space in the box is unused? Round your answer to the nearest tenth.(1 point)
Responses
3,900 mm3
3,900 mm cubed
2,325.3 mm3
2,325.3 mm cubed
1,674.7 mm3
1,674.7 mm cubed
33.5 mm3
To find the volume of the marbles, we can use the formula for the volume of a sphere:
V = (4/3) * pi * r^3
where V is the volume and r is the radius. Plugging in the values, we get:
V = (4/3) * 3.14 * 2^3
V = 33.493333...
Since we can't have a fraction of a marble, we round the volume of one marble to the nearest whole number:
V ≈ 33.5 mm^3
Now, we can find the total volume of all the marbles by multiplying the volume of one marble by the number of marbles:
total volume = 33.5 mm^3 * 50 = 1675 mm^3
To find the unused space, we subtract the total volume of the marbles from the volume of the container:
unused space = 4000 mm^3 - 1675 mm^3 = 2325 mm^3
Rounding to the nearest tenth, the unused space is 2325.3 mm^3.
Therefore, the correct answer is:
- 2,325.3 mm3
- 2,325.3 mm cubed